#18589: isogeny efficiency improvement
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Reporter: cremona | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: elliptic curves | Resolution:
Keywords: isogeny | Merged in:
Authors: John Cremona | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by cremona:
Old description:
> Computation of isogenies of prime degree p is expensive when the degree
> is neither a "genus zero" prime [2,3,5,7,13] or a "hyperelliptic prime"
> [11, 17, 19, 23, 29, 31, 41, 47, 59, 71] (for these there is special code
> written). In one situation we can save time, after factoring the degree
> (p^2-1)/2 division polynomial, if there is exactly one factor of degree
> (p-1)/2, or one subset of factors whose product has that degree, then the
> factor of degree (p-1)/2 must be a kernel polynomial. Then we do not
> need to check consistency, which is very expensive.
>
> The example which led me to this was with p=89 over a quadratic number
> field, where E.isogeny_class() was taking days. After the change here
> that goes down to 3 hours. (There are 4 curves in the isogeny class and
> thec ode requires factoring the 89-division polynomial of each!) I will
> find a less extreme example for a doctest.
New description:
Computation of isogenies of prime degree p is expensive when the degree is
neither a "genus zero" prime [2,3,5,7,13] or a "hyperelliptic prime" [11,
17, 19, 23, 29, 31, 41, 47, 59, 71] (for these there is special code
written). In one situation we can save time, after factoring the degree
{{{(p^2-1)/2}}} division polynomial, if there is exactly one factor of
degree (p-1)/2, or one subset of factors whose product has that degree,
then the factor of degree (p-1)/2 must be a kernel polynomial. Then we do
not need to check consistency, which is very expensive.
The example which led me to this was with p=89 over a quadratic number
field, where E.isogeny_class() was taking days. After the change here
that goes down to 3 hours. (There are 4 curves in the isogeny class and
thec ode requires factoring the 89-division polynomial of each!) I will
find a less extreme example for a doctest.
--
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Ticket URL: <http://trac.sagemath.org/ticket/18589#comment:1>
Sage <http://www.sagemath.org>
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